According to recent studies (Rudmin, Eckhardt), one cross-cultural variable among the several that correlate with frequency of war is “domination”. This variable includes domination of rulers over subjects, upper class over lower class, men over women, masters over slaves. Riane Eisler also described such “dominator societies” in “The Chalice and the Blade”.

These patterns are thought to have come into existence when agriculture began; in fact, “war frequency” also correlates with a factor called “agricultural production”, and with another that comes close to “industrial production”. Eckhardt concludes that civilization in general, compared with a primitive life-style, is conducive to war. These correlations are not necessarily causal, but they might be – it’s just not proven. To abolish war, it might be profitable to control these variables and see if it helps.

So do we have to throw civilization overboard, including not only industry, but even agriculture? “We can’t reverse progress”, you say? But is it progress if it threatens to destroy us? If we have taken a wrong turn at a crossroads, even very far back, it is rational to go all the way back and take the correct turn. Don’t throw good money after bad, don’t succumb to the sacrifice trap…

But it may not be necessary, after all, to throw out the baby with the bath-water. With loss of industry and agriculture, we could sustain only much smaller populations. Maybe all we have to do is get rid of dominance.

As we look at natural systems, many seem to be hierarchically organized. Barnyard chickens have their pecking order, as do male apes; every hive and ant colony has its queen; our brain takes its lion’s share of blood in preference over other organs; many hormonal systems work through cascades (e.g. ACTH releasing factor to ACTH to cortisol); food chains have big creatures at the top and small ones at the bottom. Are we then doomed to operate an increasingly fascist society? Let us take a closer look at other patterns.

By criteria of normal rationality, if A is greater than B and B is greater than C, then A has to be greater than C. This is most certainly true of numbers. But if A is more beautiful than B and B is more virtuous than C. we do not know how A and C compare in either beauty or virtue. If two qualities are compared between the three entities, we can quite rationally have intransitivity, which is that A goes over B, B goes over C, but C goes over A. A children’s game, which compares 3 qualities of 3 objects, says it all: Scissors cut paper, paper wraps stone, stone breaks scissors.

We see intransitivity in action every time we fold the four flaps of a box so that each flap is under the one on its left (say) but over the one on its right, all the way around. We may have to work a bit harder on the last one to make it fit, but when it’s done, it keeps the box securely closed.

Intransitivity also figures in “the voter’s paradox”, where a voter may prefer A over B and B over C, and yet prefer C over A, if these candidates or issues are presented two at a time. Such voter preference schedules may seem irrational, but only if we see them as being compared along a single dimension (like forming a Gutman scale); but a voter may be thinking of two or more terms of comparison between the alternatives presented. One concrete example is a voter in a golf club, who prefers the building of a new club house over continuing to use the old club house (because the roof leaks in the old one), and prefers a new club house with a bar over one without a bar (because it’s cheaper to include it during construction than to have to retrofit later); yet he may finally decide that he would rather stay in the old club house and get a little wet with rain occasionally than to have to deal with drunks at the bar at all times.

While the voter’s paradox is considered to be a nuisance in theories of voting and elections, intransitivity is worth considering as a “non-dominator” pattern. The question “which is stronger: scissors, paper, or stone?” has no answer, because each is under one other object and over the other, like the four flaps of the box. There is local dominance, or dominance in a single quality only, but no universal dominance in all qualities, that could describe one of the terms of comparison as stronger or higher or better or a winner or a leader or a king.

In society, could we have division of labour without dominance? It would seem at least conceptually possible. In the play “Creighton”, the servant becomes the master when the family is shipwrecked on a desert island, because he is better able to cope with the new situation. When they are rescued, they revert to their original social roles. Could we vary our social hierarchies in a way dependent on the situation? It already happens in the army, where the officer may have a lower social rank in civilian life than the private has. Let us have the “fittest” or “fittingest” on top, but the quality of “fitness” is necessarily defined by the situation or the environment, in society as well as in nature.

Most suggestions for getting rid of dominance opt for “equality”, but this suggests a gray sameness and uniformity. Division of labour is functional and some people will always be better at some tasks than other people are, but worse at some other tasks. It seems more “ecological” to find for each person’s talents a particular niche, in which he/she has sets of superiors and inferiors for various talents. The overall consequence would be approximate equality, and certainly absence of dominance; and perhaps society would fit together as tightly and securely as the four flaps of a box. A good visual symbol is four right hands in a circle, each clasping the wrist of one neighbour while being clasped at the wrist by the other neighbour. We note that an intransitive relationship has to be a cycle; and like a simple knot (which also illustrates intransitivity) has to have at least a certain minimum degree of complexity.

With the recognition of cyclicity comes the realization how “natural” intransitivity can be, since nature abounds in cycles. It is cycles that maintain active homeostasis. Carbon to methane to carbon to carbon dioxide and back, with all the in-between stages of half-reduced and half-oxidized, has no “better” or “superior” stages – the whole cycle is of value, and the continual circulation of matter through the cycle from stage to stage is of value. Hierarchies exist locally: methane is the most reduced and carbon dioxide is the most oxidized, but they harmonize in the overall pattern.

We do not follow a linear pattern A over B over C over D etc., as in the pecking order of dominance; not a linear arrow to a final goal. Rather we practice pattern maintenance in a dynamic way, like a good Prigoginian dissipative structure should. This, not “progress”, is truly sustainable, truly equitable, and truly peaceful.

The Borromean rings (see illustration, facing) are a perfect example of intransitivity. Ring A lies entirely above ring B, ring B lies entirely above ring C, but ring C lies entirely above ring A. None of the three pairs of rings, AB, BC, CA are linked, but if the three rings are interrelated in this intransitive way, the three are linked like a knot – like a good interdependent society of independent individuals.

If the structure is made of physical rings, either each ring has to be slightly twisted or deformed, or (with rigid rings), the structure is not co-planar. In either case it has a profound beauty.